I am clueless about this one...can someone help me with it ...thanks
Business and finance. The demand equation for a certain type of printer is given by
D = -200p + 35,000
The supply equation is predicted to be
S= -6p^2 + 400p – 20,000
Find the equilibrium price.
Don't you set demand equal to supply, and solve for p?
Ihave no idea i even looked all over the book for other similar problems and just nothing i found.
To find the equilibrium price, you are correct that you need to set the demand equal to the supply and solve for the price (p). Here's how you can do it step by step:
Step 1: Set the demand equation (D) equal to the supply equation (S):
-200p + 35,000 = -6p^2 + 400p - 20,000
Step 2: Rearrange the equation to make it quadratic (in the form ax^2 + bx + c = 0):
-6p^2 + (400p - 200p) + (35,000 + 20,000) = 0
-6p^2 + 200p + 55,000 = 0
Step 3: Divide the entire equation by -1 to make the coefficient of p^2 positive:
6p^2 - 200p - 55,000 = 0
Step 4: Solve the quadratic equation. You can use the quadratic formula or factoring method to find the values of p. Let's use the quadratic formula:
p = [ -b ± √(b^2 - 4ac) ] / 2a
For our equation, a = 6, b = -200, and c = -55,000. Plugging in these values into the formula, we get:
p = [ -(-200) ± √((-200)^2 - 4(6)(-55,000))] / (2 * 6)
Simplifying further:
p = [ 200 ± √(40,000 + 1,320,000)] / 12
p = [ 200 ± √1,360,000] / 12
p = [ 200 ± 1,166.19] / 12
Now, you'll have two values for p. Let's calculate them separately:
p₁ = (200 + 1166.19) / 12 = 135.52
p₂ = (200 - 1166.19) / 12 = -80.52
Step 5: Identify the valid solution. Since price cannot be negative, the valid equilibrium price is p = 135.52.
Therefore, the equilibrium price for the given demand and supply equations is approximately $135.52.
I hope this explanation helps you understand how to solve for the equilibrium price using the given demand and supply equations.